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Monte Carlo Methods for

Accelerator Simulation and

Photon Beam Modeling

AAPM Summer School 2006Windsor, ON

Part I Daryoush Sheikh-Bagheri, PhD

Allegheny General HospitalPittsburgh, PA

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A sample of work done … 1• McCall et al used MC simulations to study the effects of various targets and flattening filters on the mean energy of photon beams (McCall, McIntyre, and Turnbull 1978).

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A sample of work done … 2• Petti investigated the electron contamination in photon beams (Petti et al. 1983) by simulating a treatment machine head in great detail using a cylindrical geometry package to approximate various components of the linear accelerator.

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A sample of work done … 3Mohan et al calculated photon spectra and fluence distributions from several accelerators (Mohan, Chui, and Lidofsky 1985).

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A sample of work done … 4Rogers et al (1988) investigated the sources of electron contamination in a 60Co beam.

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A sample of work done … 5Chaney et al simulated a 6MV photon accelerator to study the origins of head scatter (Chaney, Cullip, and Gabriel 1994).

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A sample of work done … 6• Lovelock et al (1994) simulated the photon beams from a ScanditronixMM50 machine to obtain the beam characteristics needed for treatment planning (Lovelock et al. 1994).

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A sample of work done … 7

• Sixel and Faddegon simulated a Therac-6 treatment head in radiosurgerymode using a cylindrically symmetric geometry (Sixel and Faddegon 1995).

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A sample of work done … 8• To study the differential beam hardening effect of the flattening filter, Lee simulated the 6 MV beam from a Varian Clinac 2100C accelerator using the EGS4 code (Lee 1997).

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A sample of work done … 9

• To determine the parameters in their photon source model used for dose calculation in the PEREGRINE system, Hartmann-Siantar et al simulated linacs using MCNP and the EGS4/BEAM code (Hartmann-Siantar 1997 & 2001).

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A sample of work done … 10

• DeMarco et al simulated photon beams from Philips SL-15/25 linear accelerators to obtain the phase space information for patient dose calculation (DeMarco, Solberg, and Smathers 1998).

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A sample of work done … 11• A more detailed report on the simulation of clinical photon beams using the EGS4/BEAM code was given by Sheikh-Bagheri (Sheikh-Bagheri 1999).• Some of the results will be discussed in detail in this talk

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A sample of work done … 12• Another MC system, PENELOPE, was also used to simulate photon beams from a Saturne 43 accelerator (Mazurier et al. 1999).

• Balog et al simulated the multileaf collimator (MLC) interleaf transmission by simulating the NOMOS MIMiC MLC attached to a GE Orion 4 MV linear accelerator (Balog et al. 1999).

• The treatment head of a Siemens MXE accelerator was simulated to design a new flattening filter for the 6 MV photon beam for this machine (Faddegon, O'Brien, and Mason 1999).

• Verhaegen et al applied the EGS4/BEAM code to the simulation of radiotherapy kV x-ray units (Verhaegen et al. 1999).

• Detailed reviews on MC simulation and modeling of clinical photon and electron beams for radiation therapy (Ma and Jiang 1999) and (Verhaegenand Seuntjens 2003).

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Accelerator Simulation• Several general-purpose MC code systems have been

used for radiotherapy beam modeling including ETRAN/ITS, EGS4, EGSnrc, MCNP4/MCNP5, PENELOPE, GEANT3/ GEANT4. (see Verhaegen and Seuntjens 2003).

• Allow building an accelerator from a series of components

• Allow for tagging particles based on the interactions they undergo and location of the interactions

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Simulation Accuracy

• A goal of 2%/2 mm practical and adequate (Chetty et al., 2006)

• Agreement better than 1% could be achieved by fine-tuning

• Probably overkill (since 2–3% dosimetricuncertainty in machine commissioning)

• Overall accuracy of 5%/5 mm feasible, if relative doses to 3%/3 mm and calibration dose to 2%/2 mm (Faddegon et al. 1998)

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Simulation Efficiency

• Typically, 108 – 109 photons are needed for treatment planning dose calculation

• The total CPU time required to simulate all the photon and electron energies clinically used will be days using a state of the art desktop computer

• Iterative process of fine-tuning electron incident energy and other accelerator parameters for all the beams

• The real leap has been made possible by the use of various variance reduction techniques

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Simulation Geometry

• All the required materials and geometric data to build the MC simulation geometry:

– have to be obtained either from the linac manufacturer(s) or

– measured directly

• Note: – accelerator repairs, improvements or updates – same model may not have the same exact components – different scattering foils, flattening filters, monitor

chambers or applicators.

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Phase Space Information

• properties such as energy, particle type, position, direction, progeny and statistical weight

• standardized format recommended by IAEA consultant group (Capote et al. 2006).

phase_spacenoun

(physics) an ideal space in which the coordinate dimensions represent the variables that are required to describe a system or substance

- WordReference.com

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energy IQ X Y U V W weight zlast latch (set=1, not set=0) 5.967 -1 3.796 0.798 0.052 -0.016 0.999 1.00000 0.000000E+00 00000 00000000000000000001101 06.403 -1 3.095 -3.189 -0.022 -0.007 1.000 1.00000 1.042001E+01 00000 00000000000000000001101 06.204 -1 -4.636 -3.742 -0.079 -0.003 0.997 1.00000 1.972275E+01 00000 00000000000000000001101 06.182 -1 0.256 3.038 -0.029 0.081 0.996 1.00000 1.082931E+0 00000 00000000000000000001101 00.422 0 8.982 -13.394 0.092 -0.170 0.981 1.00000 1.091982E+01 00011 00000000000000000000101 11.526 0 3.427 2.474 0.033 0.020 0.999 1.00000 1.078395E+01 00011 00000000000000000000101 15.304 0 9.304 0.659 0.100 0.008 0.995 1.00000 1.055505E+01 00011 00000000000000000000101 1

1.979 0 -8.925 0.226 -0.170 -0.037 0.985 1.00000 2.830493E+01 00110 00000000000000000101101 14.721 -1 0.126 -2.427 0.037 -0.058 0.998 1.00000 1.062370E+01 00000 00000000000000000001101 05.659 -1 -1.835 -4.749 -0.021 -0.108 0.994 1.00000 1.076090E+01 00000 00000000000000000001101 0

5.997 -1 -3.670 1.640 -0.093 -0.009 0.996 1.00000 1.109481E+01 00000 00000000000000000001101 06.159 -1 1.974 -2.846 0.046 -0.023 0.999 1.00000 1.087926E+01 00000 00000000000000000001101 00.249 0 -2.551 -8.385 0.288 -0.134 0.948 1.00000 8.184898E+01 00111 00000000000000001001101 13.667 -1 -2.465 -0.315 0.693 0.298 0.656 1.00000 9.381655E+01 00000 00000000000000010011101 00.265 0 -6.770 7.748 0.299 0.346 0.889 1.00000 9.471067E+01 00011 00000000000000010000101 11.260 0 3.249 -9.367 0.018 -0.146 0.989 1.00000 1.970133E+01 00101 00000000000000000011101 15.803 -1 -1.859 0.138 -0.026 0.017 1.000 1.00000 1.978862E+01 00000 00000000000000000011101 00.128 0 2.488 -2.189 -0.187 -0.061 0.980 1.00000 8.195136E+01 00111 00000000000000001001101 13.404 -1 4.750 -0.711 0.248 -0.213 0.945 1.00000 5.642510E+01 00000 00000000000000001001101 03.440 -1 -11.33 14.605 -0.092 0.078 0.993 1.00000 5.641980E+01 00000 00000000000000001001101 0

Phase space file: one particle /line in binary form

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IAEA recommended phase space variables (Capote et al. 2006).

m*(Real*4) (m ≥ 0)Extra storage space for variables (e.g., EGS ZLAST)

Float_extra

n*(Integer*4) (n ≥ 0)Extra storage space for variables (e.g., EGS LATCH, incremental history number,

PENELOPE ILB, etc.)

Integer_extraLogical*1Signifies if particle belongs to new historyIs_new_historyLogical*1Sign of W (direction cosine in Z)Sign_of_W

Integer*2Type of the particleParticle_type

Real*4Particle statistical weightStatistical_weight

Real*4Kinetic energy in MeVEReal*4Direction cosine along YVReal*4Direction cosine along XUReal*4Position in Z direction in cmZReal*4Position in Y direction in cmYReal*4Position in X direction in cmX

Type of variable returned

MeaningVariable

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target

primary collimator

flattening filtermonitor chamber

mirror

y jaws

x jaws

multileaf collimator

wedge

incident electron beam

target

primary collimator

flattening filtermonitor chamber

mirror

y jaws

x jaws

multileaf collimator

wedge

incident electron beam

Typical components of a MC model of a medical linac

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“Reference” Phase Space Files

RPSDs available on the RPC website (http://rpc.mdanderson.org)

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How accurate would a Monte Carlo simulation of photon beams

turn out to be … if we had “all” the information that we typically need to model a linac?

Lessons learned from BEAM code photon beam benchmark study …

… a while ago …

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Med Phys27(10):

2256–2266

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The effective point of measurement

Med Phys27(10):

2256–2266

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More Recent Studies of Build-up Dose

Listed:• Cross section inaccuracies (radiative corrections)

Investigated in detail: • The effective point of measurement (EPOM)• EPOM shift is dependent on every detail of the ionization chamber (cavity length and radius, wall material density and thickness, central electrode radius) in addition to the beam energy and field size

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More Recent Studies of Build-up Dose

Ruled out:• unknown electron source in the head model• contaminating neutrons; • faulty cross section data; • (x,p) reactions.

• Showed a simplified model of triplet production can affect the build-up dose for the 18 MV beam • But still not sufficiently

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10 MV

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Sensitivity of Measurable Beam Characteristics to the Model of

the Accelerator

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Influence of Initial Electron Characteristics

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Where electrons start …

Courtesy of Tim Waldron, M. D. Anderson

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… where electrons continue …

Courtesy of Tim Waldron, M. D. Anderson

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Radial Distribution of electron beam-on-target

• Not typically provided confidently by manufacturers

• The user may end up deriving it from dosimetricmeasurements.

• Mainly influences the off-axis factors

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The effect of the intensity dist. of the electron beam

dmaxThe effect of the electron beam-on-target radial intensitydistribution on dose profiles

Med. Phys. Vol 27

No 10., October 2000

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Variation ofOAFs with

the FWHM ofthe incident

electron beam radial

intensitydistribution

Medical Physics, Vol. 29,

No. 3, March 2002

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Energy and Energy Distribution of electron beam-on-target

• Both DD and OAF are sensitive to the energy variation

• As the energy increases the horns reduce

• Varying the FWHM of the energy distribution of the electron beam-on-target from 0-20% not observable on the calculated OAFs and very small effect on the depth-dose curves

• The effect of asymmetrical electron energy spectrum on the photon build-up DD although relatively small, is observable (Sheikh-Bagheri and Rogers 2002a).

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The effect of Mean Energy of the electron beam-on-target, on the in-air OAF

Medical Physics, Vol. 29, No. 3,

March 2002

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Variation ofOAFs withthe energy spread of

the incident electron beam

Medical Physics, Vol. 29,

No. 3, March 2002

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Are even finer details of the e- beam energy distribution observable?

14 MeV 14 MeV

14.7 MeV 14.7 MeV

Medical Physics, Vol. 29, No. 3, March 2002

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Influence of Accelerator components

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… the target• Keall et al. (2003) • Increasing the target density hardens the 6 MV DD

and softens the 18 MV DD• Small change in density affects the DD, but not

significantly• Varying the density from 18 to 17 g/cm3 -> 1.7%

difference in dose profiles for the 6 MV and 0.3% for the 18 MV beams

• Sheikh-Bagheri et al. (2000 and 2002a) • The target lateral dimensions not important if the

target width is much larger than the lateral spread of electrons in the target or the radius of the upstream opening of the primary collimator

• Otherwise OAFs affected

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Variation ofOAFs with

a variation of 0.01 cm in the

upstream radius of the

primary collimator

Medical Physics, Vol. 29,

No. 3, March 2002

…the primary collimator

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… the flattening filter• The manufacturers commonly provide very precise

dimensions of the flattening filter.• Mistakes can happen; blueprint said FF made of Copper• Density affects the “in-air” and consequently “in-

phantom” dose profiles dramatically• The density of different types of pure W varies by

more than 1 g/cm3

• Better know the density to better than 0.25 g/cm3

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Variation ofOAFs with

the material of the FF

Medical Physics, Vol. 29,

No. 3, March 2002

Copper

Lead

Tungsten

Measured

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Variation ofOAFs with

the density of the FF

Medical Physics, Vol. 29,

No. 3, March 2002

17 g/cm3

18 g/cm3

Tungsten, 19.3 g/cm3

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• investigated the influence of buildup caps on the in-air OAR measurements

• Confirmed the usefulnessof in-air OAFs in MC linac

modeling

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Facts:

• Both OAF and DD are sensitive to electron beam-on-target energy …

• The OAFs (and therefore dose profiles) are also sensitive to the electron beam-on-target radial intensity distribution

• However the DD is not

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One approach …

• First start with a best estimate for both • Using central-axis relative depth-doses find ->

the energy of the electron beam and its energy distribution

• Then use off-axis factors to determine the radial intensity distribution and fine tune the electron beam energy

• Note: the accuracy of the derived model parameters is directly affected by the accuracy of the measured dosimetric data

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MC Calculated ( ) Siemens measured ( )

Comparison of the calculated and measured PDD data.

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Diff between calc and meas

PDDs

Local dose difference

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Normalized to Dmax

Diff between calc and meas

PDDs

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Calculated and Measured In-Air Off-Axis Factors

Solid lines: derived parameters

Blue-dashed: suggested parameters

Symbols: TG-46

Medical Physics, Vol. 29, No. 3, March 2002

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Comparison of the derived and the manufacturer suggested electron beam characteristics

of some commercial medical linear accelerators

LINAC Nominal accelerating

potential (MV)

Suggested electron energy (MeV)

(and spread %) (Manufacturer)

Derived electron energy (MeV)

(and spread %)

Nominal electron beam FWHM

(cm)

Derived electron beam FWHM

(cm)

Varian Clinac low-

energy

4 4 (3%) 3.7 (3%) 0.1 0.15

Varian Clinac high-

energy

6 10 15 18

6 (3%) 10 (3%) 15 (3%) 18 (3%)

5.7 (3%) 10.5 (3%) 14.5 (3 %) 18.3 (3 %)

0.1 0.1 0.1 0.1

0.2 0.15 0.17 0.11

Philips SL25 6 25

6 (17%) 19 (5%)

6.3 (17%) 19.0 (5%)

0.1 0.1

0.11 0.10

Siemens KD 6 18

5.53 (14%)-> 6.6 12.87 (14%)->14.68

6.8 (14%) 14.7 (14%)

0.2 0.2

0.32 0.10

Medical Physics, Vol. 29, No. 3, March 2002

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Important to model … when benchmarking

• Exact electron beam energy• FWHM of the electron beam intensity distribution

– the details of the shape to a lesser extent• Geometrical details … of course• Material and density of the flattening filter• Exact jaw settings• Exact angle of incidence of the e- beam on target• Finite size of detector (build-up dose)• The above list not exhaustive …

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… not as important …

• Electron beam divergence (< 5 mrad)• Exact FWHM of electron beam energy (< 5 %)

– the details of the shape to some extent• Electron multiple scattering in target • Finite size of detector (for a reasonably small ion chamber) • Variation of SPRwater

air with depth or laterally• Energy response of the ion chamber

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Modeling MLCs in Detail

Examples:

McGill NOMOS

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MC calculated IMRT Patterns with MLC-120measured PEREGRINE

A

B

C

CORVUS Beam Utilities

NOMOS/NAS Medical

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2-D Dose AnalysisCT Phantom: 512 x 512 x 83Dose Grid: 150 x 150 x 150 with 0.047 cm spacing. 1.5 % statistics16 P-III 1 GHz 2050 MUs, 60 segments

to keep the jaws open to 5x5

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tongue-and-groove effect

Without With

Jun Deng et al., Stanford

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So much for “brute force” MC …

Next, Charlie will talk about the design and utilization of

MC Source Models …

Thank you for your attention !